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2010-04-08T13:39:53+02:00
Sin(α)=2cos(γ)*sin(β)

pomocnicze zmienne:
γ=(x+y)/2
β=(x-y)/2
2cos(γ)*sin(β)=2cos(x+y)/2*sin(x-y)/2=
=sinx+siny

ale
γ=(x+y)/2 →2γ=x+y
β=(x-y)/2 →2β=x-y

x=β+γ=180-α
y=γ-β
sin(α)=sin(180-α)+sin(γ-β)
sin(α)=sin(α)+sin(γ-β)
sin(γ-β)=0
γ-β=0
γ=β

Cbdu


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